{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"08_TF_Logistic_Regression","provenance":[{"file_id":"https://github.com/madewithml/basics/blob/master/notebooks/08_Logistic_Regression.ipynb","timestamp":1582817842854}],"collapsed_sections":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"QsUcHSE0TcRM","colab_type":"text"},"source":["# Logistic Regression\n","\n","In this lesson, we're going to implement logistic regression for a classification task where we want to probabilistically determine the outcome for a given set of inputs. We will understand the basic math behind it, implement it in just NumPy and then in TensorFlow + Keras."]},{"cell_type":"markdown","metadata":{"id":"G-CQd9joTxwB","colab_type":"text"},"source":["<div align=\"left\">\n","<a href=\"https://github.com/madewithml/basics/blob/master/notebooks/08_Logistic_Regression/08_TF_Logistic_Regression.ipynb\" role=\"button\"><img class=\"notebook-badge-image\" src=\"https://img.shields.io/static/v1?label=&amp;message=View%20On%20GitHub&amp;color=586069&amp;logo=github&amp;labelColor=2f363d\"></a>&nbsp;\n","<a href=\"https://colab.research.google.com/github/madewithml/basics/blob/master/notebooks/08_Logistic_Regression/08_TF_Logistic_Regression.ipynb\"><img class=\"notebook-badge-image\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"></a>\n","</div>"]},{"cell_type":"markdown","metadata":{"id":"VoMq0eFRvugb","colab_type":"text"},"source":["# Overview"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"orlWnRz2-wyO"},"source":["Logistic regression is just an extension on linear regression (both are generalized linear methods). We will still learn to model a line (plane) that models $y$ given $X$. Except now we are dealing with classification problems as opposed to regression problems so we want classification probabilities. We'll be using the softmax operation to normalize our logits ($XW$) to derive probabilities.\n","\n","Our goal is to learn a logistic model $\\hat{y}$ that models $y$ given $X$. \n","\n","$ \\hat{y} = \\frac{e^{XW_y}}{\\sum_j e^{XW}} $ \n","* $\\hat{y}$ = prediction | $\\in \\mathbb{R}^{NX1}$ ($N$ is the number of samples)\n","* $X$ = inputs | $\\in \\mathbb{R}^{NXD}$ ($D$ is the number of features)\n","* $W$ = weights | $\\in \\mathbb{R}^{DXC}$ ($C$ is the number of classes)\n","\n","This function is known as the multinomial logistic regression or the softmax classifier. The softmax classifier will use the linear equation ($z=XW$) and normalize it (using the softmax function) to produce the probabiltiy for class y given the inputs.\n","\n","**NOTE**: We'll leave the bias weights out for now to avoid complicating the backpropagation calculation."]},{"cell_type":"markdown","metadata":{"id":"T4Y55tpzIjOa","colab_type":"text"},"source":["* **Objective:**  Predict the probability of class $y$ given the inputs $X$. The softmax classifier normalizes the linear outputs to determine class probabilities. \n","* **Advantages:**\n","  * Can predict class probabilities given a set on inputs.\n","* **Disadvantages:**\n","  * Sensitive to outliers since objective is to minimize cross entropy loss. Support vector machines ([SVMs](https://towardsdatascience.com/support-vector-machine-vs-logistic-regression-94cc2975433f)) are a good alternative to counter outliers.\n","* **Miscellaneous:** Softmax classifier is going to used widely in neural network architectures as the last layer since it produces class probabilities."]},{"cell_type":"markdown","metadata":{"id":"3SYAo2FHl1I3","colab_type":"text"},"source":["# Data"]},{"cell_type":"markdown","metadata":{"id":"00B5uEM8Tb0d","colab_type":"text"},"source":["## Load data"]},{"cell_type":"markdown","metadata":{"id":"sYNIM3PxQGgo","colab_type":"text"},"source":["We'll used some synthesized data to train our models on. The task is to determine whether a tumor will be benign (harmless) or malignant (harmful) based on leukocyte (white blood cells) count and blood pressure. Note that this is a synethic dataset that has no clinical relevance."]},{"cell_type":"code","metadata":{"id":"A8rspXhNEgrL","colab_type":"code","colab":{}},"source":["import matplotlib.pyplot as plt\n","import numpy as np\n","import pandas as pd\n","from pandas.plotting import scatter_matrix\n","import urllib"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"zbcxlUHbT2z0","colab_type":"code","colab":{}},"source":["SEED = 1234\n","DATA_FILE = 'tumors.csv'"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"nchxHc9sX6UJ","colab_type":"code","colab":{}},"source":["# Set seed for reproducibility\n","np.random.seed(SEED)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"7sp_tSyItf1_","colab_type":"code","colab":{}},"source":["# Download data from GitHub to this notebook's local drive\n","url = \"https://raw.githubusercontent.com/madewithml/basics/master/data/tumors.csv\"\n","response = urllib.request.urlopen(url)\n","html = response.read()\n","with open(DATA_FILE, 'wb') as fp:\n","    fp.write(html)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"7alqmyzXtgE8","colab_type":"code","outputId":"2aeee600-3e2e-44e2-d4c6-e9f602b58e06","executionInfo":{"status":"ok","timestamp":1583940928114,"user_tz":420,"elapsed":1215,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":204}},"source":["# Read from CSV to Pandas DataFrame\n","df = pd.read_csv(DATA_FILE, header=0)\n","df.head()"],"execution_count":5,"outputs":[{"output_type":"execute_result","data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>leukocyte_count</th>\n","      <th>blood_pressure</th>\n","      <th>tumor_class</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>13.472969</td>\n","      <td>15.250393</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>10.805510</td>\n","      <td>14.109676</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>13.834053</td>\n","      <td>15.793920</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>9.572811</td>\n","      <td>17.873286</td>\n","      <td>malignant</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>7.633667</td>\n","      <td>16.598559</td>\n","      <td>malignant</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["   leukocyte_count  blood_pressure tumor_class\n","0        13.472969       15.250393   malignant\n","1        10.805510       14.109676   malignant\n","2        13.834053       15.793920   malignant\n","3         9.572811       17.873286   malignant\n","4         7.633667       16.598559   malignant"]},"metadata":{"tags":[]},"execution_count":5}]},{"cell_type":"code","metadata":{"id":"3aqJxfKmnYTs","colab_type":"code","colab":{}},"source":["# Define X and y\n","X = df[['leukocyte_count', 'blood_pressure']].values\n","y = df['tumor_class'].values"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"lpoF3_EgDtPl","colab_type":"code","outputId":"b9aa44b6-b495-4562-dd36-c5bb652d2d4a","executionInfo":{"status":"ok","timestamp":1583940928572,"user_tz":420,"elapsed":1271,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":279}},"source":["# Plot data\n","colors = {'benign': 'red', 'malignant': 'blue'}\n","plt.scatter(X[:, 0], X[:, 1], c=[colors[_y] for _y in y], s=25, edgecolors='k')\n","plt.xlabel('leukocyte count')\n","plt.ylabel('blood pressure')\n","plt.legend(['malignant ', 'benign'], loc=\"upper right\")\n","plt.show()"],"execution_count":7,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhg6NRrFi5bBixYrHugYVlexQZ/wqLyUkMW7cRIwaNQnx8XGIiCiCbduO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nrniBzAdcjKQ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\nnvidcy7DeOJ3zrkM44nfOecyzP8BfwdZPZ1K+7MAAAAASUVORK5CYII=\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"23rUN1uTpoc4","colab_type":"text"},"source":["## Split data"]},{"cell_type":"code","metadata":{"id":"EHcoL7fH_CsS","colab_type":"code","colab":{}},"source":["import collections\n","from sklearn.model_selection import train_test_split"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"XJA0YhzxUWPP","colab_type":"code","colab":{}},"source":["TRAIN_SIZE = 0.7\n","VAL_SIZE = 0.15\n","TEST_SIZE = 0.15\n","SHUFFLE = True"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"_Mak_supAsIV","colab_type":"text"},"source":["Splitting the dataset for classification tasks requires more than just randomly splitting into train, validation and test sets. We want to ensure that each split has a similar class distribution so that we can learn to predict well across all the classes. We can do this by specifying the `stratify` argument in [`train_test_split`](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) which will be set to the class labels."]},{"cell_type":"code","metadata":{"id":"27h91LX0pp7F","colab_type":"code","colab":{}},"source":["def train_val_test_split(X, y, val_size, test_size, shuffle):\n","    \"\"\"Split data into train/val/test datasets.\n","    \"\"\"\n","    X_train, X_test, y_train, y_test = train_test_split(\n","        X, y, test_size=test_size, stratify=y, shuffle=shuffle) # notice the `stratify=y`\n","    X_train, X_val, y_train, y_val = train_test_split(\n","        X_train, y_train, test_size=val_size, stratify=y_train, shuffle=shuffle) # notice the `stratify=y_train`\n","    return X_train, X_val, X_test, y_train, y_val, y_test"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"D4fy2vUjr-Qe","colab_type":"code","outputId":"5a672b05-269e-4383-8934-4a1dfd9701b4","executionInfo":{"status":"ok","timestamp":1583940933076,"user_tz":420,"elapsed":341,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":102}},"source":["# Create data splits\n","X_train, X_val, X_test, y_train, y_val, y_test = train_val_test_split(\n","    X=X, y=y, val_size=VAL_SIZE, test_size=TEST_SIZE, shuffle=SHUFFLE)\n","class_counts = dict(collections.Counter(y))\n","print (f\"X_train: {X_train.shape}, y_train: {y_train.shape}\")\n","print (f\"X_val: {X_val.shape}, y_val: {y_val.shape}\")\n","print (f\"X_test: {X_test.shape}, y_test: {y_test.shape}\")\n","print (f\"Sample point: {X_train[0]} → {y_train[0]}\")\n","print (f\"Classes: {class_counts}\")"],"execution_count":11,"outputs":[{"output_type":"stream","text":["X_train: (722, 2), y_train: (722,)\n","X_val: (128, 2), y_val: (128,)\n","X_test: (150, 2), y_test: (150,)\n","Sample point: [18.01865938 15.48133647] → benign\n","Classes: {'malignant': 611, 'benign': 389}\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"lLHG5_vpHQ3d","colab_type":"text"},"source":["## Label encoder"]},{"cell_type":"markdown","metadata":{"id":"YGWO8zDCHTFp","colab_type":"text"},"source":["You'll notice that our class labels are text. We need to encode them into integers so we can use them in our models. We're going to the scikit-learn's [LabelEncoder](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html#sklearn.preprocessing.LabelEncoder) to do this. "]},{"cell_type":"code","metadata":{"id":"KPIsL1kAHkhu","colab_type":"code","colab":{}},"source":["from sklearn.preprocessing import LabelEncoder"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hcfHtYFtHkmo","colab_type":"code","colab":{}},"source":["# Output vectorizer\n","y_tokenizer = LabelEncoder()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"4hbPtvg4HoqE","colab_type":"code","outputId":"8ac25431-b8ff-46f6-d5e0-f5b3cfa5e18e","executionInfo":{"status":"ok","timestamp":1583940935240,"user_tz":420,"elapsed":227,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Fit on train data\n","y_tokenizer = y_tokenizer.fit(y_train)\n","classes = y_tokenizer.classes_\n","print (f\"classes: {classes}\")"],"execution_count":14,"outputs":[{"output_type":"stream","text":["classes: ['benign' 'malignant']\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"U7MTxcrcHotG","colab_type":"code","outputId":"3e506954-2482-4b7f-8f94-1039f8e5e5e9","executionInfo":{"status":"ok","timestamp":1583940937363,"user_tz":420,"elapsed":323,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Convert labels to tokens\n","print (f\"y_train[0]: {y_train[0]}\")\n","y_train = y_tokenizer.transform(y_train)\n","y_val = y_tokenizer.transform(y_val)\n","y_test = y_tokenizer.transform(y_test)\n","print (f\"y_train[0]: {y_train[0]}\")"],"execution_count":15,"outputs":[{"output_type":"stream","text":["y_train[0]: benign\n","y_train[0]: 0\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"sXHboWkUAIjI","colab_type":"code","outputId":"7df1c7af-457f-4437-e463-b873d1ce9b0f","executionInfo":{"status":"ok","timestamp":1583940937966,"user_tz":420,"elapsed":376,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Class weights\n","counts = collections.Counter(y_train)\n","class_weights = {_class: 1.0/count for _class, count in counts.items()}\n","print (f\"class counts: {counts},\\nclass weights: {class_weights}\")"],"execution_count":16,"outputs":[{"output_type":"stream","text":["class counts: Counter({1: 441, 0: 281}),\n","class weights: {0: 0.0035587188612099642, 1: 0.0022675736961451248}\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"nkAmzEwVHs6E","colab_type":"text"},"source":["**NOTE**: Class weights are useful for weighting the loss function during training. It tells the model to focus on samples from an under-represented class. The loss section below will show how to incorporate these weights."]},{"cell_type":"markdown","metadata":{"id":"IodMyhnAJUg_","colab_type":"text"},"source":["## Standardize data"]},{"cell_type":"markdown","metadata":{"id":"QRhNHi9YJfDm","colab_type":"text"},"source":["We need to standardize our data (zero mean and unit variance) in order to optimize quickly. We're only going to standardize the inputs X because our outputs y are class values."]},{"cell_type":"code","metadata":{"id":"rjIz1KKYJWI7","colab_type":"code","colab":{}},"source":["from sklearn.preprocessing import StandardScaler"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hP6VTXSiJWM1","colab_type":"code","colab":{}},"source":["# Standardize the data (mean=0, std=1) using training data\n","X_scaler = StandardScaler().fit(X_train)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"kn2SDd28Jwna","colab_type":"code","colab":{}},"source":["# Apply scaler on training and test data (don't standardize outputs for classification)\n","X_train = X_scaler.transform(X_train)\n","X_val = X_scaler.transform(X_val)\n","X_test = X_scaler.transform(X_test)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"zBAu7GkJJwq8","colab_type":"code","outputId":"8298a506-92df-4e92-9d89-635062ed8a45","executionInfo":{"status":"ok","timestamp":1583940942384,"user_tz":420,"elapsed":433,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":119}},"source":["# Check (means should be ~0 and std should be ~1)\n","print (f\"X_train[0]: mean: {np.mean(X_train[:, 0], axis=0):.1f}, std: {np.std(X_train[:, 0], axis=0):.1f}\")\n","print (f\"X_train[1]: mean: {np.mean(X_train[:, 1], axis=0):.1f}, std: {np.std(X_train[:, 1], axis=0):.1f}\")\n","print (f\"X_val[0]: mean: {np.mean(X_val[:, 0], axis=0):.1f}, std: {np.std(X_val[:, 0], axis=0):.1f}\")\n","print (f\"X_val[1]: mean: {np.mean(X_val[:, 1], axis=0):.1f}, std: {np.std(X_val[:, 1], axis=0):.1f}\")\n","print (f\"X_test[0]: mean: {np.mean(X_test[:, 0], axis=0):.1f}, std: {np.std(X_test[:, 0], axis=0):.1f}\")\n","print (f\"X_test[1]: mean: {np.mean(X_test[:, 1], axis=0):.1f}, std: {np.std(X_test[:, 1], axis=0):.1f}\")"],"execution_count":20,"outputs":[{"output_type":"stream","text":["X_train[0]: mean: 0.0, std: 1.0\n","X_train[1]: mean: -0.0, std: 1.0\n","X_val[0]: mean: 0.1, std: 1.0\n","X_val[1]: mean: 0.1, std: 1.0\n","X_test[0]: mean: -0.1, std: 1.0\n","X_test[1]: mean: -0.1, std: 1.0\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"CYH7kRTd9WoJ","colab_type":"text"},"source":["# NumPy\n","\n","Now that we have our data prepared, we'll first implement logistic regression using just NumPy. This will let us really understand the underlying operations. It's normal to find the math and code in this section slightly complex. You can still read each of the steps to build intuition for when we implement this using TensorFlow + Keras."]},{"cell_type":"markdown","metadata":{"id":"Y-gUbD71-yiX","colab_type":"text"},"source":["Our goal is to learn a logistic model $\\hat{y}$ that models $y$ given $X$. \n","\n","$ \\hat{y} = \\frac{e^{XW_y}}{\\sum e^{XW}} $ \n","* $\\hat{y}$ = prediction | $\\in \\mathbb{R}^{NX1}$ ($N$ is the number of samples)\n","* $X$ = inputs | $\\in \\mathbb{R}^{NXD}$ ($D$ is the number of features)\n","* $W$ = weights | $\\in \\mathbb{R}^{DXC}$ ($C$ is the number of classes)"]},{"cell_type":"markdown","metadata":{"id":"6wcc5lbdH_Hi","colab_type":"text"},"source":["We are going to use multinomial logistic regression even though our task only involves two classes because you can generalize the softmax classifier to any number of classes."]},{"cell_type":"markdown","metadata":{"id":"YOTrUTpwWWba","colab_type":"text"},"source":["## Initialize weights"]},{"cell_type":"markdown","metadata":{"id":"o-Os5f8mad5_","colab_type":"text"},"source":["1. Randomly initialize the model's weights $W$."]},{"cell_type":"code","metadata":{"id":"jdPe3f01Wg6X","colab_type":"code","colab":{}},"source":["INPUT_DIM = X_train.shape[1] # X is 2-dimensional\n","NUM_CLASSES = len(classes) # y has two possibilities (begign or malignant)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"6x4heep29c_F","colab_type":"code","outputId":"852f4a84-58fa-4433-97ac-26a7cb8a3b4c","executionInfo":{"status":"ok","timestamp":1583940968682,"user_tz":420,"elapsed":264,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Initialize random weights\n","W = 0.01 * np.random.randn(INPUT_DIM, NUM_CLASSES)\n","b = np.zeros((1, NUM_CLASSES))\n","print (f\"W: {W.shape}\")\n","print (f\"b: {b.shape}\")"],"execution_count":22,"outputs":[{"output_type":"stream","text":["W: (2, 2)\n","b: (1, 2)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"FdnkMO9AWsNB","colab_type":"text"},"source":["## Model"]},{"cell_type":"markdown","metadata":{"id":"7Fh8YOJjae28","colab_type":"text"},"source":["2. Feed inputs $X$ into the model to receive the logits ($z=XW$). Apply the softmax operation on the logits to get the class probabilies $\\hat{y}$ in one-hot encoded form. For example, if there are three classes, the predicted class probabilities could look like [0.3, 0.3, 0.4]. \n","  * $ \\hat{y} = softmax(z) = softmax(XW) = \\frac{e^{XW_y}}{\\sum_j e^{XW}} $"]},{"cell_type":"code","metadata":{"id":"EXQkZOwW-otw","colab_type":"code","outputId":"60262772-8e4b-4783-c533-17c303fa0afd","executionInfo":{"status":"ok","timestamp":1583940975520,"user_tz":420,"elapsed":491,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Forward pass [NX2] · [2X2] + [1,2] = [NX2]\n","logits = np.dot(X_train, W) + b\n","print (f\"logits: {logits.shape}\")\n","print (f\"sample: {logits[0]}\")"],"execution_count":23,"outputs":[{"output_type":"stream","text":["logits: (722, 2)\n","sample: [0.01817675 0.00635562]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"Ak9FfYIJ-ozJ","colab_type":"code","outputId":"76d03621-4943-4482-87f9-44b2005ddf3c","executionInfo":{"status":"ok","timestamp":1583940975675,"user_tz":420,"elapsed":251,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Normalization via softmax to obtain class probabilities\n","exp_logits = np.exp(logits)\n","y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","print (f\"y_hat: {y_hat.shape}\")\n","print (f\"sample: {y_hat[0]}\")"],"execution_count":24,"outputs":[{"output_type":"stream","text":["y_hat: (722, 2)\n","sample: [0.50295525 0.49704475]\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"qQ39Xr8QW22V","colab_type":"text"},"source":["## Loss"]},{"cell_type":"markdown","metadata":{"id":"VxxORg12amXv","colab_type":"text"},"source":[" 3. Compare the predictions $\\hat{y}$ (ex.  [0.3, 0.3, 0.4]]) with the actual target values $y$ (ex. class 2 would look like [0, 0, 1]) with the objective (cost) function to determine loss $J$. A common objective function for logistics regression is cross-entropy loss. \n","\n","  * $J(\\theta) = - \\sum_i ln(\\hat{y_i}) = - \\sum_i ln (\\frac{e^{X_iW_y}}{\\sum_j e^{X_iW}}) $"]},{"cell_type":"code","metadata":{"id":"_dfuMmW2Y01f","colab_type":"code","outputId":"df854186-4e76-42a9-9efa-2359c671fb60","executionInfo":{"status":"ok","timestamp":1583940977237,"user_tz":420,"elapsed":422,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Loss\n","correct_class_logprobs = -np.log(y_hat[range(len(y_hat)), y_train])\n","loss = np.sum(correct_class_logprobs) / len(y_train)\n","print (f\"loss: {loss:.2f}\")"],"execution_count":25,"outputs":[{"output_type":"stream","text":["loss: 0.69\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"iIz5JF8rW5uM","colab_type":"text"},"source":["## Gradients"]},{"cell_type":"markdown","metadata":{"id":"g9nWUa-3b2lw","colab_type":"text"},"source":["4. Calculate the gradient of loss $J(\\theta)$ w.r.t to the model weights. Let's assume that our classes are mutually exclusive (a set of inputs could only belong to one class).\n"," * $\\frac{\\partial{J}}{\\partial{W_j}} = \\frac{\\partial{J}}{\\partial{\\hat{y}}}\\frac{\\partial{\\hat{y}}}{\\partial{W_j}} = - \\frac{1}{\\hat{y}}\\frac{\\partial{\\hat{y}}}{\\partial{W_j}} = - \\frac{1}{\\frac{e^{XW_y}}{\\sum_j e^{XW}}}\\frac{\\sum_j e^{XW}e^{XW_y}0 - e^{XW_y}e^{XW_j}X}{(\\sum_j e^{XW})^2} = \\frac{Xe^{XW_j}}{\\sum_j e^{XW}} = X\\hat{y}$\n","  * $\\frac{\\partial{J}}{\\partial{W_y}} = \\frac{\\partial{J}}{\\partial{\\hat{y}}}\\frac{\\partial{\\hat{y}}}{\\partial{W_y}} = - \\frac{1}{\\hat{y}}\\frac{\\partial{\\hat{y}}}{\\partial{W_y}} = - \\frac{1}{\\frac{e^{XW_y}}{\\sum_j e^{XW}}}\\frac{\\sum_j e^{XW}e^{XW_y}X - e^{W_yX}e^{XW_y}X}{(\\sum_j e^{XW})^2} = \\frac{1}{\\hat{y}}(X\\hat{y} - X\\hat{y}^2) = X(\\hat{y}-1)$"]},{"cell_type":"code","metadata":{"id":"9_-LGJWwZqhW","colab_type":"code","colab":{}},"source":["# Backpropagation\n","dscores = y_hat\n","dscores[range(len(y_hat)), y_train] -= 1\n","dscores /= len(y_train)\n","dW = np.dot(X_train.T, dscores)\n","db = np.sum(dscores, axis=0, keepdims=True)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"Fuw-7BVrW-_M","colab_type":"text"},"source":["## Update weights"]},{"cell_type":"markdown","metadata":{"id":"QaOhLrqib7t9","colab_type":"text"},"source":["5. Update the weights  𝑊  using a small learning rate  𝛼. The updates willpenalize the probabiltiy for the incorrect classes (j) and encourage a higher probability for the correct class (y).\n","  * $W_j = W_j - \\alpha\\frac{\\partial{J}}{\\partial{W_j}}$"]},{"cell_type":"code","metadata":{"id":"8pDGJRmQXC39","colab_type":"code","colab":{}},"source":["LEARNING_RATE = 1e-1"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"qy6LjHNPZqe1","colab_type":"code","colab":{}},"source":["# Update weights\n","W += -LEARNING_RATE * dW\n","b += -LEARNING_RATE * db"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"TsxBN1l8XUVn","colab_type":"text"},"source":["## Training"]},{"cell_type":"code","metadata":{"id":"wa9N6rLtXVYB","colab_type":"code","colab":{}},"source":["NUM_EPOCHS = 50"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"AFjnVvCqb_Kk","colab_type":"text"},"source":["6. Repeat steps 2 - 5 to minimize the loss and train the model."]},{"cell_type":"code","metadata":{"id":"vCipe3EhZqbl","colab_type":"code","outputId":"4dcba73b-10a8-4967-bbcb-bf6eb1c1053f","executionInfo":{"status":"ok","timestamp":1583941278683,"user_tz":420,"elapsed":783,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":102}},"source":["# Initialize random weights\n","W = 0.01 * np.random.randn(INPUT_DIM, NUM_CLASSES)\n","b = np.zeros((1, NUM_CLASSES))\n","\n","# Training loop\n","for epoch_num in range(NUM_EPOCHS):\n","\n","    # Forward pass [NX2] · [2X2] = [NX2]\n","    logits = np.dot(X_train, W) + b\n","    \n","    # Normalization via softmax to obtain class probabilities\n","    exp_logits = np.exp(logits)\n","    y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","\n","    # Loss\n","    correct_class_logprobs = -np.log(y_hat[range(len(y_hat)), y_train])\n","    loss = np.sum(correct_class_logprobs) / len(y_train)\n","\n","    # show progress\n","    if epoch_num%10 == 0:\n","        # Accuracy\n","        y_pred = np.argmax(logits, axis=1)\n","        accuracy =  np.mean(np.equal(y_train, y_pred))\n","        print (f\"Epoch: {epoch_num}, loss: {loss:.3f}, accuracy: {accuracy:.3f}\")\n","\n","    # Backpropagation\n","    dscores = y_hat\n","    dscores[range(len(y_hat)), y_train] -= 1\n","    dscores /= len(y_train)\n","    dW = np.dot(X_train.T, dscores)\n","    db = np.sum(dscores, axis=0, keepdims=True)\n","\n","    # Update weights\n","    W += -LEARNING_RATE * dW\n","    b += -LEARNING_RATE * db"],"execution_count":57,"outputs":[{"output_type":"stream","text":["Epoch: 0, loss: 0.698, accuracy: 0.202\n","Epoch: 10, loss: 0.452, accuracy: 0.978\n","Epoch: 20, loss: 0.351, accuracy: 0.979\n","Epoch: 30, loss: 0.296, accuracy: 0.981\n","Epoch: 40, loss: 0.261, accuracy: 0.981\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"2zHB-mHA1-Uh","colab_type":"text"},"source":["Since we're taking the argmax, we can just calculate logits since normalization won't change which index has the higher value. "]},{"cell_type":"code","metadata":{"id":"TpE3oDpIhhBH","colab_type":"code","colab":{}},"source":["class LogisticRegressionFromScratch():\n","    def predict(self, x):\n","        logits = np.dot(x, W) + b\n","        exp_logits = np.exp(logits)\n","        y_hat = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n","        return y_hat"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-6T8rm1bw_Sw","colab_type":"code","colab":{}},"source":["# Evaluation\n","model = LogisticRegressionFromScratch()\n","logits_train = model.predict(X_train)\n","pred_train = np.argmax(logits_train, axis=1)\n","logits_test = model.predict(X_test)\n","pred_test = np.argmax(logits_test, axis=1)"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Smy3DxJazGFm","colab_type":"code","outputId":"35773fde-0f61-43ae-b74a-dae83e819ee5","executionInfo":{"status":"ok","timestamp":1583941281758,"user_tz":420,"elapsed":786,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Training and test accuracy\n","train_acc =  np.mean(np.equal(y_train, pred_train))\n","test_acc = np.mean(np.equal(y_test, pred_test))\n","print (f\"train acc: {train_acc:.2f}, test acc: {test_acc:.2f}\")"],"execution_count":60,"outputs":[{"output_type":"stream","text":["train acc: 0.98, test acc: 0.94\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"Cv-Dxp4AxeWh","colab_type":"code","colab":{}},"source":["def plot_multiclass_decision_boundary(model, X, y, savefig_fp=None):\n","    \"\"\"Plot the multiclass decision boundary for a model that accepts 2D inputs.\n","\n","    Arguments:\n","        model {function} -- trained model with function model.predict(x_in).\n","        X {numpy.ndarray} -- 2D inputs with shape (N, 2).\n","        y {numpy.ndarray} -- 1D outputs with shape (N,).\n","    \"\"\"\n","    # Axis boundaries\n","    x_min, x_max = X[:, 0].min() - 0.1, X[:, 0].max() + 0.1\n","    y_min, y_max = X[:, 1].min() - 0.1, X[:, 1].max() + 0.1\n","    xx, yy = np.meshgrid(np.linspace(x_min, x_max, 101),\n","                         np.linspace(y_min, y_max, 101))\n","\n","    # Create predictions\n","    x_in = np.c_[xx.ravel(), yy.ravel()]\n","    y_pred = model.predict(x_in)\n","    y_pred = np.argmax(y_pred, axis=1).reshape(xx.shape)\n","\n","    # Plot decision boundary\n","    plt.contourf(xx, yy, y_pred, cmap=plt.cm.Spectral, alpha=0.8)\n","    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.RdYlBu)\n","    plt.xlim(xx.min(), xx.max())\n","    plt.ylim(yy.min(), yy.max())\n","\n","    # Plot\n","    if savefig_fp:\n","        plt.savefig(savefig_fp, format='png')"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Z7RorJHHxfW7","colab_type":"code","outputId":"f3347dbb-200f-410d-d04d-5722a0a0383f","executionInfo":{"status":"ok","timestamp":1583941285195,"user_tz":420,"elapsed":1449,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["# Visualize the decision boundary\n","plt.figure(figsize=(12,5))\n","plt.subplot(1, 2, 1)\n","plt.title(\"Train\")\n","plot_multiclass_decision_boundary(model=model, X=X_train, y=y_train)\n","plt.subplot(1, 2, 2)\n","plt.title(\"Test\")\n","plot_multiclass_decision_boundary(model=model, X=X_test, y=y_test)\n","plt.show()"],"execution_count":62,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAsEAAAE/CAYAAACnwR6AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niFNOuLuR8NcvYpl2a8qTGHl0omYrTQlG+eAjwW6/C2o4MktLnrouR5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btv9Y3XjlCKBSK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\nQThzeBu2Dp8fHRH8lGJzWTn3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7scVQuAK9OAKtK6WO/3djH3tJbZu3DO93FUV38Qw/Zdn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crhEJwyhDcNrcTm/vkt52eFLZuzzftEhhx0NljbX3p0OGkcHe5Wlb83CHnsQzHnRRSSlLr5mun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\nQmCC\n","text/plain":["<Figure size 864x360 with 2 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"QW5piG-XCz1N","colab_type":"text"},"source":["Credit for the plotting functions and the intuition behind all this is due to [CS231n](http://cs231n.github.io/neural-networks-case-study/), one of the best courses for machine learning. Now let's implement logistic regression with TensorFlow + Keras."]},{"cell_type":"markdown","metadata":{"id":"7Cy3efR7s7HD","colab_type":"text"},"source":["# TensorFlow + Keras"]},{"cell_type":"markdown","metadata":{"id":"hsnnH37eYxql","colab_type":"text"},"source":["Now that we've implemented logistic regression with Numpy, let's do the same with TensorFlow + Keras. "]},{"cell_type":"code","metadata":{"id":"mWEfPoXzYxym","colab_type":"code","colab":{}},"source":["%tensorflow_version 2.x\n","import tensorflow as tf"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"jVS_h2-cZW6U","colab_type":"code","colab":{}},"source":["# Set seed for reproducibility\n","tf.random.set_seed(SEED)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"-h-dlCTaYowa","colab_type":"text"},"source":["## Model"]},{"cell_type":"markdown","metadata":{"id":"CuGUAtHkyFBv","colab_type":"text"},"source":["We will be using [Dense](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/keras/layers/Dense) layers to recreate the same model."]},{"cell_type":"code","metadata":{"id":"7-vm9AZm1_f9","colab_type":"code","colab":{}},"source":["from tensorflow.keras.layers import Dense\n","from tensorflow.keras.layers import Input\n","from tensorflow.keras.models import Model\n","from tensorflow.keras.utils import plot_model"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"p63Ws2STYolf","colab_type":"code","colab":{}},"source":["class LogisticRegression(Model):\n","    def __init__(self, num_classes):\n","        super(LogisticRegression, self).__init__(name='logistic_regression')\n","        self.fc1 = Dense(units=num_classes, activation='softmax', name='W')\n","        \n","    def call(self, x_in, training=False):\n","        y_pred = self.fc1(x_in)\n","        return y_pred\n","    \n","    def summary(self, input_shape):\n","        x_in = Input(shape=input_shape, name='X')\n","        summary = Model(inputs=x_in, outputs=self.call(x_in), name=self.name)\n","        return plot_model(summary, show_shapes=True) # forward pass"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"6kJgaEqIcyHR","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":201},"outputId":"3496609c-f622-475c-9999-db39904f8011","executionInfo":{"status":"ok","timestamp":1583941289007,"user_tz":420,"elapsed":1117,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}}},"source":["# Initialize model\n","model = LogisticRegression(num_classes=NUM_CLASSES)\n","model.summary(input_shape=(INPUT_DIM,))"],"execution_count":67,"outputs":[{"output_type":"execute_result","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAASUAAAC4CAIAAAAqim0JAAAABmJLR0QA/wD/AP+gvaeTAAAfZklE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1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\nvz/SGVSSxQAAAABJRU5ErkJggg==\n","text/plain":["<IPython.core.display.Image object>"]},"metadata":{"tags":[]},"execution_count":67}]},{"cell_type":"markdown","metadata":{"id":"alKyigoqa9w9","colab_type":"text"},"source":["## Loss"]},{"cell_type":"markdown","metadata":{"id":"NLkVlnQJaQ4q","colab_type":"text"},"source":["Our loss will be the [SparseCategoricalCrossentropy](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/keras/losses/SparseCategoricalCrossentropy). "]},{"cell_type":"code","metadata":{"id":"HVGEm4habEuN","colab_type":"code","colab":{}},"source":["from tensorflow.keras.losses import SparseCategoricalCrossentropy"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"wux5LwEGbFI7","colab_type":"code","outputId":"0125ad48-763f-474b-d857-f07e196f9629","executionInfo":{"status":"ok","timestamp":1583941289917,"user_tz":420,"elapsed":510,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["scce = tf.keras.losses.SparseCategoricalCrossentropy()\n","ground_truth = tf.convert_to_tensor([0, 1, 2])\n","probabilities = tf.convert_to_tensor([[.9, .05, .05], [.5, .89, .6], [.05, .01, .94]])\n","loss = scce(ground_truth, probabilities)\n","print (loss.numpy())"],"execution_count":69,"outputs":[{"output_type":"stream","text":["0.32396814\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"f9oyIzgccYLy","colab_type":"text"},"source":["## Metrics"]},{"cell_type":"code","metadata":{"id":"6D-lJ7TVZgAR","colab_type":"code","colab":{}},"source":["from tensorflow.keras.metrics import SparseCategoricalAccuracy"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"rwzXNiPZcaCU","colab_type":"code","outputId":"eb8baf99-f306-45c8-d051-7f8cad5acb11","executionInfo":{"status":"ok","timestamp":1583941290950,"user_tz":420,"elapsed":478,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["m = SparseCategoricalAccuracy()\n","m.update_state(ground_truth, probabilities)\n","print( m.result().numpy()) "],"execution_count":71,"outputs":[{"output_type":"stream","text":["1.0\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"m2zZs70qaOWn","colab_type":"text"},"source":["## Optimizer"]},{"cell_type":"code","metadata":{"id":"DWeLpGaIa64l","colab_type":"code","colab":{}},"source":["from tensorflow.keras.optimizers import Adam"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"oqzC6hRla7FN","colab_type":"code","colab":{}},"source":["optimizer=Adam(lr=LEARNING_RATE)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"BTjMYiOQcqNb","colab_type":"text"},"source":["## Training"]},{"cell_type":"code","metadata":{"id":"1X9BaZWwdD0P","colab_type":"code","colab":{}},"source":["BATCH_SIZE = 32"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"hA7Oz97NAe8A","colab_type":"code","colab":{}},"source":["# Compile\n","model.compile(optimizer=Adam(lr=LEARNING_RATE),\n","              loss=SparseCategoricalCrossentropy(),\n","              metrics=[SparseCategoricalAccuracy()])"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"FBWtqKCDtXHN","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":1000},"outputId":"4c4d5e72-6fc4-4deb-f5af-dc469f58051c","executionInfo":{"status":"ok","timestamp":1583941297118,"user_tz":420,"elapsed":3504,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}}},"source":["# Training\n","model.fit(x=X_train, \n","          y=y_train,\n","          validation_data=(X_val, y_val),\n","          epochs=NUM_EPOCHS,\n","          batch_size=BATCH_SIZE,\n","          class_weight=class_weights, \n","          shuffle=False,\n","          verbose=1)"],"execution_count":76,"outputs":[{"output_type":"stream","text":["WARNING:tensorflow:sample_weight modes were coerced from\n","  ...\n","    to  \n","  ['...']\n","WARNING:tensorflow:sample_weight modes were coerced from\n","  ...\n","    to  \n","  ['...']\n","Train on 722 samples, validate on 128 samples\n","Epoch 1/50\n","722/722 [==============================] - 0s 513us/sample - loss: 8.3439e-04 - sparse_categorical_accuracy: 0.8615 - val_loss: 4.1483e-04 - val_sparse_categorical_accuracy: 0.9688\n","Epoch 2/50\n","722/722 [==============================] - 0s 54us/sample - loss: 2.5897e-04 - sparse_categorical_accuracy: 0.9834 - val_loss: 2.8280e-04 - val_sparse_categorical_accuracy: 0.9766\n","Epoch 3/50\n","722/722 [==============================] - 0s 62us/sample - loss: 1.9570e-04 - sparse_categorical_accuracy: 0.9861 - val_loss: 2.3468e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 4/50\n","722/722 [==============================] - 0s 73us/sample - loss: 1.7173e-04 - sparse_categorical_accuracy: 0.9875 - val_loss: 2.1131e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 5/50\n","722/722 [==============================] - 0s 67us/sample - loss: 1.5492e-04 - sparse_categorical_accuracy: 0.9875 - val_loss: 1.9432e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 6/50\n","722/722 [==============================] - 0s 74us/sample - loss: 1.4234e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.8063e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 7/50\n","722/722 [==============================] - 0s 63us/sample - loss: 1.3253e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.6964e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 8/50\n","722/722 [==============================] - 0s 63us/sample - loss: 1.2462e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.6068e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 9/50\n","722/722 [==============================] - 0s 66us/sample - loss: 1.1810e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.5321e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 10/50\n","722/722 [==============================] - 0s 58us/sample - loss: 1.1262e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.4687e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 11/50\n","722/722 [==============================] - 0s 57us/sample - loss: 1.0796e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.4143e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 12/50\n","722/722 [==============================] - 0s 63us/sample - loss: 1.0394e-04 - sparse_categorical_accuracy: 0.9889 - val_loss: 1.3671e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 13/50\n","722/722 [==============================] - 0s 57us/sample - loss: 1.0043e-04 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.3258e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 14/50\n","722/722 [==============================] - 0s 57us/sample - loss: 9.7343e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.2893e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 15/50\n","722/722 [==============================] - 0s 61us/sample - loss: 9.4607e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.2568e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 16/50\n","722/722 [==============================] - 0s 54us/sample - loss: 9.2165e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.2278e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 17/50\n","722/722 [==============================] - 0s 57us/sample - loss: 8.9973e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.2016e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 18/50\n","722/722 [==============================] - 0s 60us/sample - loss: 8.7994e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.1780e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 19/50\n","722/722 [==============================] - 0s 69us/sample - loss: 8.6200e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.1565e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 20/50\n","722/722 [==============================] - 0s 61us/sample - loss: 8.4566e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.1369e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 21/50\n","722/722 [==============================] - 0s 61us/sample - loss: 8.3072e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.1190e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 22/50\n","722/722 [==============================] - 0s 59us/sample - loss: 8.1703e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.1025e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 23/50\n","722/722 [==============================] - 0s 73us/sample - loss: 8.0443e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.0873e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 24/50\n","722/722 [==============================] - 0s 72us/sample - loss: 7.9280e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.0732e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 25/50\n","722/722 [==============================] - 0s 64us/sample - loss: 7.8205e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.0602e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 26/50\n","722/722 [==============================] - 0s 56us/sample - loss: 7.7209e-05 - sparse_categorical_accuracy: 0.9903 - val_loss: 1.0482e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 27/50\n","722/722 [==============================] - 0s 64us/sample - loss: 7.6283e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 1.0369e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 28/50\n","722/722 [==============================] - 0s 52us/sample - loss: 7.5420e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 1.0264e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 29/50\n","722/722 [==============================] - 0s 57us/sample - loss: 7.4616e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 1.0166e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 30/50\n","722/722 [==============================] - 0s 55us/sample - loss: 7.3865e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 1.0074e-04 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 31/50\n","722/722 [==============================] - 0s 57us/sample - loss: 7.3162e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.9880e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 32/50\n","722/722 [==============================] - 0s 64us/sample - loss: 7.2503e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.9070e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 33/50\n","722/722 [==============================] - 0s 60us/sample - loss: 7.1885e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.8309e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 34/50\n","722/722 [==============================] - 0s 58us/sample - loss: 7.1303e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.7592e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 35/50\n","722/722 [==============================] - 0s 61us/sample - loss: 7.0757e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.6916e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 36/50\n","722/722 [==============================] - 0s 61us/sample - loss: 7.0242e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.6277e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 37/50\n","722/722 [==============================] - 0s 60us/sample - loss: 6.9756e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.5674e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 38/50\n","722/722 [==============================] - 0s 59us/sample - loss: 6.9298e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.5102e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 39/50\n","722/722 [==============================] - 0s 58us/sample - loss: 6.8865e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.4561e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 40/50\n","722/722 [==============================] - 0s 67us/sample - loss: 6.8455e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.4047e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 41/50\n","722/722 [==============================] - 0s 62us/sample - loss: 6.8067e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.3560e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 42/50\n","722/722 [==============================] - 0s 52us/sample - loss: 6.7700e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.3097e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 43/50\n","722/722 [==============================] - 0s 61us/sample - loss: 6.7352e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.2657e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 44/50\n","722/722 [==============================] - 0s 53us/sample - loss: 6.7022e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.2238e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 45/50\n","722/722 [==============================] - 0s 63us/sample - loss: 6.6709e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.1839e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 46/50\n","722/722 [==============================] - 0s 57us/sample - loss: 6.6411e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.1459e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 47/50\n","722/722 [==============================] - 0s 62us/sample - loss: 6.6129e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.1096e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 48/50\n","722/722 [==============================] - 0s 61us/sample - loss: 6.5860e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.0750e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 49/50\n","722/722 [==============================] - 0s 61us/sample - loss: 6.5604e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.0420e-05 - val_sparse_categorical_accuracy: 0.9844\n","Epoch 50/50\n","722/722 [==============================] - 0s 60us/sample - loss: 6.5360e-05 - sparse_categorical_accuracy: 0.9917 - val_loss: 9.0105e-05 - val_sparse_categorical_accuracy: 0.9844\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["<tensorflow.python.keras.callbacks.History at 0x7f4eb0061940>"]},"metadata":{"tags":[]},"execution_count":76}]},{"cell_type":"markdown","metadata":{"id":"Ufw6JQVLcuSS","colab_type":"text"},"source":["**NOTE**: We used the `class_weights` from earlier which will be used with our loss function to account for any class imbalances (our dataset doesn't suffer from this issue)."]},{"cell_type":"markdown","metadata":{"id":"dM7iYW8ANYjy","colab_type":"text"},"source":["## Evaluation"]},{"cell_type":"code","metadata":{"id":"uFXbczqu8Rno","colab_type":"code","colab":{}},"source":["import itertools\n","import matplotlib.pyplot as plt\n","from sklearn.metrics import accuracy_score\n","from sklearn.metrics import classification_report\n","from sklearn.metrics import confusion_matrix"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-RnQrNaKQhWJ","colab_type":"code","colab":{}},"source":["def plot_confusion_matrix(y_true, y_pred, classes, cmap=plt.cm.Blues):\n","    \"\"\"Plot a confusion matrix using ground truth and predictions.\"\"\"\n","    # Confusion matrix\n","    cm = confusion_matrix(y_true, y_pred)\n","    cm_norm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]\n","\n","    #  Figure\n","    fig = plt.figure()\n","    ax = fig.add_subplot(111)\n","    cax = ax.matshow(cm, cmap=plt.cm.Blues)\n","    fig.colorbar(cax)\n","\n","    # Axis\n","    plt.title(\"Confusion matrix\")\n","    plt.ylabel(\"True label\")\n","    plt.xlabel(\"Predicted label\")\n","    ax.set_xticklabels([''] + classes)\n","    ax.set_yticklabels([''] + classes)\n","    ax.xaxis.set_label_position('bottom') \n","    ax.xaxis.tick_bottom()\n","\n","    # Values\n","    thresh = cm.max() / 2.\n","    for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n","        plt.text(j, i, f\"{cm[i, j]:d} ({cm_norm[i, j]*100:.1f}%)\",\n","                 horizontalalignment=\"center\",\n","                 color=\"white\" if cm[i, j] > thresh else \"black\")\n","\n","    # Display\n","    plt.show()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-jZtTd7F6_ps","colab_type":"code","outputId":"2894000a-37e6-471a-f1a3-4d096a2b32a3","executionInfo":{"status":"ok","timestamp":1583941306300,"user_tz":420,"elapsed":410,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["# Predictions\n","pred_train = model.predict(X_train) \n","pred_test = model.predict(X_test)\n","print (f\"sample probability: {pred_test[0]}\")\n","pred_train = np.argmax(pred_train, axis=1)\n","pred_test = np.argmax(pred_test, axis=1)\n","print (f\"sample class: {pred_test[0]}\")"],"execution_count":79,"outputs":[{"output_type":"stream","text":["sample probability: [2.3825736e-04 9.9976176e-01]\n","sample class: 1\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"sEjansj78Rqe","colab_type":"code","outputId":"c2cd10b8-bedd-4723-eb77-25f4075b967c","executionInfo":{"status":"ok","timestamp":1583941306919,"user_tz":420,"elapsed":278,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Accuracy\n","train_acc = accuracy_score(y_train, pred_train)\n","test_acc = accuracy_score(y_test, pred_test)\n","print (f\"train acc: {train_acc:.2f}, test acc: {test_acc:.2f}\")"],"execution_count":80,"outputs":[{"output_type":"stream","text":["train acc: 0.99, test acc: 0.97\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"t9uDMe_Dh4cs","colab_type":"code","outputId":"fa2d7836-7d0b-4327-8057-19a1d812d5f2","executionInfo":{"status":"ok","timestamp":1583941308855,"user_tz":420,"elapsed":1554,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["# Visualize the decision boundary\n","plt.figure(figsize=(12,5))\n","plt.subplot(1, 2, 1)\n","plt.title(\"Train\")\n","plot_multiclass_decision_boundary(model=model, X=X_train, y=y_train)\n","plt.subplot(1, 2, 2)\n","plt.title(\"Test\")\n","plot_multiclass_decision_boundary(model=model, X=X_test, y=y_test)\n","plt.show()"],"execution_count":81,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAsEAAAE/CAYAAACnwR6AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbvuuEOJHTYzpVJOL57BWWt/sXis6z7XDtkvrxJ4LnYgtJ6AVtfL1uS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IgjiZcaAAEtMvv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\nQmCC\n","text/plain":["<Figure size 864x360 with 2 Axes>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"WijzY-vDNbE9","colab_type":"text"},"source":["So far we looked at accuracy as the metric that determines our mode's level of performance. But we have several other options when it comes to  evaluation metrics.\n","\n","<div align=\"left\">\n","<img src=\"https://raw.githubusercontent.com/madewithml/images/master/basics/08_Logistic_Regression/metrics.png\" width=\"350\">\n","</div>\n","\n","<small>Image credit: \"Precisionrecall\" by Walber</small>"]},{"cell_type":"markdown","metadata":{"id":"80MwyE0yOr-k","colab_type":"text"},"source":["The metric we choose really depends on the situation.\n","positive - true, 1, tumor, issue, etc., negative - false, 0, not tumor, not issue, etc.\n","\n","$\\text{accuracy} = \\frac{TP+TN}{TP+TN+FP+FN}$ \n","\n","$\\text{recall} = \\frac{TP}{TP+FN}$ → (how many of the actual issues did I catch)\n","\n","$\\text{precision} = \\frac{TP}{TP+FP}$ → (out of all the things I said were issues, how many were actually issues)\n","\n","$F_1 = 2 * \\frac{\\text{precision }  *  \\text{ recall}}{\\text{precision } + \\text{ recall}}$\n","\n","where: \n","* TP: # of samples predicted to be positive and were actually positive\n","* TN: # of samples predicted to be negative and were actually negative\n","* FP: # of samples predicted to be positive but were actually negative\n","* FN: # of samples predicted to be negative but were actually positive"]},{"cell_type":"code","metadata":{"id":"8N8jPq_Cy2hp","colab_type":"code","outputId":"dd7076e8-6fbd-46ff-b158-07bc9ed1ee25","executionInfo":{"status":"ok","timestamp":1583941313152,"user_tz":420,"elapsed":1324,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":459}},"source":["# Classification report\n","plot_confusion_matrix(y_true=y_test, y_pred=pred_test, classes=classes)\n","print (classification_report(y_test, pred_test))"],"execution_count":82,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAV4AAAEhCAYAAAA3X8gOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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w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\nJJgCr4hIgv0/nXKj3OUNtbwAAAAASUVORK5CYII=\n","text/plain":["<Figure size 432x288 with 2 Axes>"]},"metadata":{"tags":[]}},{"output_type":"stream","text":["              precision    recall  f1-score   support\n","\n","           0       0.94      1.00      0.97        58\n","           1       1.00      0.96      0.98        92\n","\n","    accuracy                           0.97       150\n","   macro avg       0.97      0.98      0.97       150\n","weighted avg       0.98      0.97      0.97       150\n","\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"9v6zc1_1PWnz","colab_type":"text"},"source":["## Inference"]},{"cell_type":"code","metadata":{"id":"kX9428-EPUzx","colab_type":"code","outputId":"1ffec64f-9ab6-49e8-a77e-b520a0ec1416","executionInfo":{"status":"ok","timestamp":1583941314583,"user_tz":420,"elapsed":227,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":80}},"source":["# Inputs for inference\n","X_infer = pd.DataFrame([{'leukocyte_count': 13, 'blood_pressure': 12}])\n","X_infer.head()"],"execution_count":83,"outputs":[{"output_type":"execute_result","data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>leukocyte_count</th>\n","      <th>blood_pressure</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>13</td>\n","      <td>12</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["   leukocyte_count  blood_pressure\n","0               13              12"]},"metadata":{"tags":[]},"execution_count":83}]},{"cell_type":"code","metadata":{"id":"3qY6buxLKb2o","colab_type":"code","outputId":"f3a8ef98-b370-4701-e16e-00a3ac9b9869","executionInfo":{"status":"ok","timestamp":1583941316166,"user_tz":420,"elapsed":443,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Standardize\n","X_infer = X_scaler.transform(X_infer)\n","print (X_infer)"],"execution_count":84,"outputs":[{"output_type":"stream","text":["[[-0.66523095 -3.08638693]]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"7O5PbOAvXTzF","colab_type":"code","outputId":"0b6cde2e-6c4e-4db5-95ee-2d4a0161116a","executionInfo":{"status":"ok","timestamp":1583941318005,"user_tz":420,"elapsed":1297,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["# Predict\n","y_infer = model.predict(X_infer)\n","_class = np.argmax(y_infer)\n","print (f\"The probability that you have a {classes[_class]} tumor is {y_infer[0][_class]*100.0:.0f}%\")"],"execution_count":85,"outputs":[{"output_type":"stream","text":["The probability that you have a benign tumor is 98%\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"8PLPFFP67tvL","colab_type":"text"},"source":["# Unscaled weights"]},{"cell_type":"markdown","metadata":{"id":"_XYBW85WIdKy","colab_type":"text"},"source":["Note that only X was standardized.\n","\n","$\\hat{y}_{unscaled} = b_{scaled} + \\sum_{j=1}^{k}W_{{scaled}_j}x_{{scaled}_j}$\n","* $x_{scaled} = \\frac{x_j - \\bar{x}_j}{\\sigma_j}$\n","\n","$\\hat{y}_{unscaled} = b_{scaled} + \\sum_{j=1}^{k} W_{{scaled}_j} (\\frac{x_j - \\bar{x}_j}{\\sigma_j}) $\n","\n","$\\hat{y}_{unscaled} = (b_{scaled} - \\sum_{j=1}^{k} W_{{scaled}_j}\\frac{\\bar{x}_j}{\\sigma_j}) +  \\sum_{j=1}^{k} (\\frac{W_{{scaled}_j}}{\\sigma_j})x_j$\n","\n","In the expression above, we can see the expression $\\hat{y}_{unscaled} = W_{unscaled}x + b_{unscaled} $\n","\n","* $W_{unscaled} = \\sum_{j=1}^{k} (\\frac{W_{{scaled}_j}}{\\sigma_j}) $\n","\n","* $b_{unscaled} = b_{scaled} - \\sum_{j=1}^{k} W_{{scaled}_j}\\frac{\\bar{x}_j}{\\sigma_j}$"]},{"cell_type":"code","metadata":{"id":"KTSpxbwy7ugl","colab_type":"code","outputId":"c6261397-21fd-43bb-aadc-2126dd0f3114","executionInfo":{"status":"ok","timestamp":1583941324492,"user_tz":420,"elapsed":461,"user":{"displayName":"Goku Mohandas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjMIOf3R_zwS_zZx4ZyPMtQe0lOkGpPOEUEKWpM7g=s64","userId":"00378334517810298963"}},"colab":{"base_uri":"https://localhost:8080/","height":68}},"source":["# Unstandardize weights \n","W = model.layers[0].get_weights()[0]\n","b = model.layers[0].get_weights()[1]\n","W_unscaled = W / X_scaler.scale_\n","b_unscaled = b - np.sum((W_unscaled * X_scaler.mean_))\n","print (W_unscaled)\n","print (b_unscaled)"],"execution_count":86,"outputs":[{"output_type":"stream","text":["[[ 3.06098186 -8.58274608]\n"," [-1.27760317  3.09602949]]\n","[54.613728 60.382847]\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"PbcuwPdKEMlK","colab_type":"text"},"source":["---\n","Share and discover ML projects at <a href=\"https://madewithml.com/\">Made With ML</a>.\n","\n","<div align=\"left\">\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://github.com/madewithml/basics\"><img src=\"https://img.shields.io/github/stars/madewithml/basics.svg?style=social&label=Star\"></a>&nbsp;\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://www.linkedin.com/company/madewithml\"><img src=\"https://img.shields.io/badge/style--5eba00.svg?label=LinkedIn&logo=linkedin&style=social\"></a>&nbsp;\n","<a class=\"ai-header-badge\" target=\"_blank\" href=\"https://twitter.com/madewithml\"><img src=\"https://img.shields.io/twitter/follow/madewithml.svg?label=Follow&style=social\"></a>\n","</div>\n","             "]}]}